Incollection,
Atmospheric turbulence as a Markov process
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
We present a stochastic analysis of observations of the backscattering
cross-section of the hydrometeors in cirrus clouds. Data are collected
with ground-based millimeter wave radar located at the Southern Great
Plains site of the Atmospheric Radiation Measurements program of the
Department of Energy.
We find evidence that the statistics of the backscattering cross-section of
the hydrometeors can be described as a Markov process. This leads to a
Fokker-Planck equation of the probability density functions of the
backscattering cross-section which is completely determined by its two
coefficients, the drift and the diffusion coefficients. We derive the
behavior of the drift and diffusion coefficients that characterize the
deterministic and stochastic parts, respectively, of the dynamics of the
probability density functions directly from the time series of observed
backscattering cross-section. Finally, we obtain that the leading terms
of the drift $\gamma$ and diffusion $\beta$ coefficients of the backscattering
cross-section signal in the upper well-mixed, neutrally stratified layer of
the cirrus cloud satisfy the relationship $\gamma=2\beta$, which is valid for
fully developed turbulence owing to the Kolmogorov -4/5 law.
